Question

Ayna and Leslie both simplified the expression.What was the mistake made by the student that was incorrect. Explain your reasoning

Answer 1

The Solution:

The given expression is

`\sqrt[]{18x^4y^5}`
`\begin{gathered} \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3)(3)(x)(x)(x)(x)(y)(y)(y)(y)(y)} \\ \\ \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3^2)(x^2)(x^2)(y^2)(y^2)(y)}=3x^2y^2\text{ }\sqrt[]{2y} \end{gathered}`

Clearly, we have that Ayna's work was wrong.

`\begin{gathered} \text{ Ayna wrote} \\ 2x^2y^2\sqrt[]{3x^2y}\text{ instead of} \\ \\ 3x^2y^2\sqrt[]{2y} \end{gathered}`

But Lesile' work is correct.

Thus, the correct answer is

`3x^2y^2\text{ }\sqrt[]{2y}`